The Serie A side have already had their first bid rejected for the former PFA player of the year - a deal believed to be in the region of €23m.
Despite Roma showing genuine interest in the Algerian star, the two clubs' valuation of the player remains someway off. Leicester value Mahrez at £50m, but Roma’s sporting director, Monchi, values him at €30m, which is still only around £26m.
There have been reports that the winger has already agreed outline personal terms with Roma. Mahrez earns £100,000 a week at Leicester, although he will decrease his weekly salary by £40,000 if he moves to Italy.
Roma are currently on the hunt for a new winger after the departure of Mohamed Salah to Liverpool for £37m – a fee which will rise to £44m.
With the Giallorossi selling Salah and midfielder Leandro Paredes to Zenit Saint Petersburg for £23.7m, the Leicester Mercury believes the Foxes will stand firm and sell Mahrez for a high price, especially with the vast sums of money which have already been paid for players this summer.
Massimiliano Vitelli, journalist at the Italian newspapers Il Tempo and La Gazzetta dello Sport, feels Monchi is under extreme pressure to land a forward this window.
“I think that Monchi is just trying to do his job but, in the end, he has to buy someone good,” he said.
Arsenal are interested in Mahrez but are yet to make an offer. Thomas Lemar of Monaco is now believed to be in Arsene Wenger’s sights.